A particle is projected with a velocity `u` making an angle `theta` with the horizontal. The instantaneous power of the gravitational force

Options

A. (a) Varies linearly with time
B. (b) Is constant throughout
C. (c) Is negative for complete path
D. (d) None of the above

Answer

A

Explanation

At any time,
`vecv=[u cos theta]hati+(u cos theta-g t)hatj`
`P=vecF.vecv=(-mghatj)*[u cos thetahatj+(u sin theta-g t)hatj]`
`=mg^2t-mgu sin theta`
Hence, power varies linearly with time.